2L 3s

"Classic" pentatonic. Perhaps the most common scale in the world.

The meantone pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly proper.

Generator						Cents	s	L-s	|L-2s|	Scale steps	Trichord	Comments
2\5						480	240	0	240	1 1 1 1 1	1 1
					11\27	488.89	222.22	44.44	177.78	6 5 5 6 5	6 5	Slendro (insofar as it resembles a MOS) would be in this region
				9\22		490.91	218.18	54.545	163.64	5 4 4 5 4	5 4
					16\39	492.31	215.38	61.54	153.85	9 7 7 9 7	9 7	No-5's superpyth/dominant is around here
			7\17			494.12	211.76	70.59	141.18	4 3 3 4 3	4 3
					19\46	495.65	208.7	78.26	130.435	11 8 8 11 8	11 8
				12\29		496.55	206.9	82.76	124.14	7 5 5 7 5	7 5
					17\41	497.56	204.88	87.8	117.07	10 7 7 10 7	10 7	Pythagorean pentatonic is around here
		5\12				500	200	100	100	3 2 2 3 2	3 2	Familiar 12-equal pentatonic (also optimum rank range: L/s=3/2)
						502.305	195.39	111.53	83.86	pi 2 pi 2 2	pi 2
					18\43	502.33	195.35	111.63	83.72	11 7 7 11 7	11 7
				13\31		503.23	193.55	116.13	77.42	8 5 5 8 5	8 5	Optimal meantone pentatonic is around here
						1200/(4-phi)	192.43	118.93	73.50	phi 1 1 phi 1	phi 1	Golden meantone
					21\50	504	192	120	72	13 8 8 13 8	13 8
			8\19			505.26	189.47	126.32	63.16	5 3 3 5 3	5 3
					19\45	506.67	186.67	133.33	53.33	12 7 7 12 7	12 7
						507.18	185.64	135.9	49.74	√3 1 √3 1 1	√3 1
				11\26		507.69	184.615	138.46	46.15	7 4 4 7 4	7 4
					14\33	509.09	181.82	145.455	36.36	9 5 5 9 5	9 5
	3\7					514.29	171.43	171.43	0	2 1 1 2 1	2 1	(Boundary of propriety: smaller generators than this are strictly proper)
					13\30	520	160	200	40	9 4 4 9 4	9 4
				10\23		521.74	156.52	208.7	52.17	7 3 3 7 3	7 3
					17\39	523.08	153.84	215.385	61.54	12 5 5 12 5	12 5
			7\16			525	150	225	75	5 2 2 5 2	5 2	5-note subset of pelog (insofar as it resembles a MOS) would be in this region
					18\41	526.83	146.34	234.15	87.8	13 5 5 13 5	13 5
						600(25+√5)/31	145.7	235.75	90.05	phi+1 1 1 phi+1 1	phi+1 1
				11\25		528	144	240	96	8 3 3 8 3	8 3
						528.88	142.24	244.405	102.17	e 1 e 1 1	e 1	L/s = e
					15\34	529.41	141.18	247.06	105.88	11 4 4 11 4	11 4
		4\9				533.33	133.33	266.67	133.33	3 1 1 3 1	3 1	L/s = 3
						535.36	129.26	276.835	147.57	pi 1 pi 1 1	pi 1	L/s = pi
					13\29	537.93	124.14	289.655	165.52	10 3 3 10 3	10 3
				9\20		540	120	240	180	7 2 2 7 2	7 2
					14\31	541.935	116.13	309.68	193.55	11 3 3 11 3	11 3
			5\11			545.45	109.09	327.27	218.18	4 1 1 4 1	4 1	L/s = 4
					11\24	550	100	350	250	9 2 2 9 2	9 2
				6\13		553.85	92.31	369.23	276.92	5 1 1 5 1	5 1
					7\15	560	80	480	400	6 1 1 6 1	6 1
1\2						600	0	600	600	1 0 0 1 0	1 0	a degenerated pentatonic scale with only 2 different steps

From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.

From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are meantone and mavila.

There is also the interesting 2.3.7 temperament that tempers out 64/63 ("no-fives dominant").